Hypersurfaces with Lr-Pointwise 1-Type Gauss Map

Автор(и)

  • Akram Mohammadpouri

DOI:

https://doi.org/10.15407/mag14.01.067

Ключові слова:

лiнеаризованi оператори Lr, Lr-точкове типу 1 гауссове вiдображення, r-мiнiмальна гiперповерхня.

Анотація

У статтi вивчаються гiперпрверхнi в 𝔼n+1, гауссове вiдображення G яких задовольняє рiвняння LrG = f(G + C) для гладкої функцiї f i постiйного вектора C, де Lr є лiнеаризованим оператором (r + 1)-ої середньої кривизни гiперповерхнi, тобто Lr(f) = Tr(Pr ○∇2f) для f ∈ 𝐶(M), а Pr є r-им перетворенням Ньютона, ∇2f є гессiаном f, LrG = (LrG1, . . . ,LrGn+1) і G = (G1, . . . ,Gn+1). Наша увага зосереджена на гiперповерхнях з постiйною (r +1)-ою средньою кривизною i постiйною середньою кривизною. Для цих класiв гiперповерхонь отримано теореми класифiкацiЁ i характеризацiї.

2010:53D02, 53C40, 53C42

Посилання

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2018-06-20

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Mohammadpouri, A. Hypersurfaces With Lr-Pointwise 1-Type Gauss Map. J. Math. Phys. Anal. Geom. 2018, 14, 67-77.

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